1. Field of the Invention
This invention relates to a method of producing a single crystal gallium nitride (GaN) substrate and a gallium nitride substrate itself for making light emitting devices of light emitting diodes (LEDs) or laser diodes (LDs) built with the nitride semiconductors consisting of the group 3-5 elements. Gallium nitride and the like (GaInN, AlInN, InAlGaN) are semiconductors having wide band gaps which correspond to blue light or blue/green light.
This application claims the priority of Japanese Patent Application No. 2000-207783 filed on Jul. 10, 2000 which is incorporated herein by refernce.
2. Description of Related Art
Blue-light LEDs making use of the nitride semiconductor (GaN, GaInN, AlInN, AlInGaN) have been already put into practice on mass scale. There is no natural single crystal GaN mineral. It has been impossible to grow gallium nitride (GaN) single crystal ingots from a GaN melt, since heating converts solid phase GaN directly into vapor phase GaN without a liquid phase. Almost all of the nitride semiconductor LEDs on sale are produced upon sapphire (xcex1-Al2O3) monocrystal (single crystal) substrates. Sapphire belongs to a trigonal symmetry group.
The GaN LEDs are fabricated by piling n-type or p-type films of GaN, GaInN, AlInN, InAlGaN or so (called xe2x80x9cGaN type filmsxe2x80x9d collectively) heteroepitaxially upon single crystal sapphire substrates. The GaN type crystals have hexagonal symmetry. GaN belongs to a different symmetry group from sapphire. Single crystal sapphire, however, turned out a very stable, suitable material as a substrate which allows the GaN type films to grow heteroepitaxially. The excellency of sapphire allows device makers to produce a plenty of inexpensive blue light or blue-green light GaN/sapphire LEDs.
However, sapphire is a very rigid material. A sapphire single crystal has no cleavage plane. Cleavage is a convenient property for cutting a wide device-made wafer into individual device chips and for making resonator mirrors of laser diodes. Lack of natural cleavage compels device makers to cut (dice) mechanically sapphire wafers crosswise and lengthwise into device chips with an application of strong forces. The dicing process incurs an extra cost and decreases a yield in the production of GaN LEDs. Uncleavability of GaN crystals subjects GaN/sapphire LDs to other difficulties besides the problems of dicing. Uncleavable GaN prevents GaN laser diodes from making resonator mirrors by natural cleavage, which invites difficulties on laser oscillation performance and on production cost.
Another difficulty originates from the fact that sapphire is an insulator. Electrical insulation of sapphire prohibits the on-sapphire LEDs from taking a vertical electrode structure which allocates top and bottom surfaces for two electrodes (anode and cathode). Instead of the common vertical electrode structure, the sapphire-carried LEDs take a horizontal electrode structure by etching partially upper films, revealing a part of an n-type GaN-type film, making a cathode on the n-type GaN-type film and producing an anode upon a top p-type GaN-type film. The n-type GaN-type film should be thick enough to allow current to flow in the horizontal direction. The n-type electrode pad should be bonded to a cathode pin by wirebonding. The extra etching, the extra thick film and an extra wirebonding raise the cost by increasing the time of fabrication and the number of steps. Furthermore, the larger chip surface required for allocating two electrodes on the same surface. This point incurs an increment of the cost.
The sapphire substrates are suffering from these difficulties. Someone proposes a use of silicon carbide (SiC) as a substrate for GaN light emitting devices (LEDs and LDs). Silicon carbide belongs to the hexagonal symmetry group like GaN. Natural cleavage accompanies a silicon carbide crystal. Natural cleavage will facilitate to cut a GaN optoelectronic device-loaded SiC wafer into individual device chips and will conveniently make resonator mirrors in GaN LDs. SiC is electrically conductive. The conductive SiC allows the vertical electrode structure which allocates top and bottom surfaces to an anode and a cathode. Silicon carbide substrates favor the fabrication process of making GaN type LEDs. Silicon carbide, however, has some drawbacks. Single crystal silicon carbide is highly expensive. The difficulty of producing SiC single crystals will jeopardize a continual, stable supply of SiC substrates. The crystalline property of GaN films grown on SiC substrates are still bad at present. SiC is not deemed to be the suitable material as a substrate of GaN light emission devices. SiC is rather inferior to sapphire as a substrate for GaN LEDs. GaN/SiC LEDs are not brought onto market yet.
Sapphire or silicon carbide as a substrate induces many dislocations and other defects in GaN type films grown thereupon owing to mismatches of lattice constants and thermal expansion coefficients between the upper films and the bottom substrate. GaN/sapphire LEDs on sale have about 1xc3x97109 cmxe2x88x922 dislocations in the GaN epitaxial films.
It is said that GaN films heteroepitaxially grown on silicon carbide (SiC) would have about 1xc3x97108 cmxe2x88x922. Plenty of dislocations induced in the GaN films cause no serious damage to the practical utility of the GaN/sapphire LEDs. The GaN/sapphire LEDs enjoy a long lifetime despite the affluence of dislocations.
However, in the case of GaN/sapphire LDs which require large current density, experiments clarify the fact that the big dislocation density forbids the on-sapphire GaN type LDs from having a long lifetime. The big current increases the dislocations and other defects. Furthermore, an LD requires resonator consisting of two parallel mirrors at both ends of a cavity. Sapphire substrates without cleavage require elaborate dicing and polishing for making flat smooth mirrors with high reflection. The fabrication of the resonator mirror would raise the cost of GaN/sapphire LDs. The high cost and short lifetime degrade sapphire as a substrate for GaN LDs. From the reasons, sapphire and silicon carbide are not the most suitable material for the substrates of GaN LDs.
The best substrate should be a gallium nitride (GaN) single crystal (monocrystal). If a wide GaN single crystal substrate were obtained, the problem of the mismatches of the lattice constant and the thermal expansion would be entirely solved. GaN has natural cleavage in {1xe2x88x92100} planes. GaN is a semiconductor. Impurity doped GaN substrates have enough conductivity. GaN substrates would be superior to sapphire substrates in cleavability and conductivity. Gallium nitride single crystals would be the most favorable substrates for GaN LDs. However, crystal growth technology has not been matured for GaN yet. It is difficult at present to produce gallium nitride single crystals with a large size sufficient for the substrates of GaN LDs.
Heating converts solid GaN not to liquid GaN but to vapor GaN. High pressure and high temperature are requisites for making a GaN melt. It is said that it would be possible to synthesize a gallium nitride single crystal from a GaN melt in a state of thermal equilibrium maintained by ultrahigh pressure and high temperature. However, even if it succeeded, the ultrahigh pressure method would synthesize only a small GaN crystal which would be insufficient for the substrate of GaN LDs. The inventors of the present invention are unaware of such a report of succeeding in making a GaN bulk single crystal by the ultrahigh pressure method. Such a liquid phase method is hopeless for supplying wide gallium nitride crystals on an industrial scale.
Someone suggested a method of covering a sapphire substrate with a mask having windows, piling gallium nitride molecules through the mask upon the sapphire substrate and making a GaN film on the sapphire in vapor phase. The mask having windows has an effect of reducing dislocations in the GaN film.
{circle around (1)} Akira Usui, xe2x80x9cThick Layer Growth of GaN by Hydride Vapor Phase Epitaxyxe2x80x9d, Electric Information Communication Society, Vol.J81-C-II, No.1, p58-64 (1998, Jan).
{circle around (2)} Akira Sakai, Akira Usui, xe2x80x9cDecrease of the dislocation density by GaN epitaxial lateral overgrowthxe2x80x9d, Japanese Journal of Applied Physics, vol.68, No.7, p774-779 (1999).
The reports suggested improvements of the vapor phase growth of GaN film upon a sapphire substrate through a window-carrying mask. They adhered to sapphire substrates. It is impossible to eliminate the sapphire substrate from the GaN film, since there is no means of removing the hard, sturdy sapphire. Thus, the final product of {circle around (1)} and {circle around (2)} is an assembly of a sapphire substrate and a GaN crystal grown upon the sapphire.
The inventors of the present invention proposed methods of making a GaN film through window-carrying mask upon a gallium arsenide (GaAs) substrate, eliminating the GaAs substrate and obtaining a freestanding GaN single crystal.
{circle around (3)} Japanese Patent Application No.9-298300 (298300/""97 )
{circle around (4)} Japanese Patent Application No.10-9008 (9008/""98)
The applications proposed methods of making a wide low-dislocation density GaN single crystal through the mask windows upon the GaAs substrate. The method of growing GaN through the window-carrying mask upon a substrate (sapphire or GaAs) is called xe2x80x9cEpitaxial Lateral Overgrowth (ELO)xe2x80x9d.
The new ELO method proposed by {circle around (3)} and {circle around (4)} produces a gallium nitride single crystal by the steps of forming a mask having plenty of striped windows or round windows on a GaAs substrate, growing a GaT film through the windows of the mask by some method (e.g., HVPE, MOCVD, MOC, etc.) upon the GaAs substrate and removing the GaAs substrate.
Among the growth methods, the inventors prefer to the HVPE (hydride vapor phase epitaxy) method. Thus, the HVPE method is now described by referring to FIG. 1. A vertically long furnace 1 contains a Ga-boat 2 including a Ga melt 3 near the top. A susceptor 4 is furnished upon a top of a shaft near the bottom in the vertical furnace 1. A substrate 5 is mounted upon the susceptor 4. Here, the substrate is a (111) GaAs single crystal. A cylindrical heater 6 encloses the tall furnace 1. The top of the furnace 1 has two gas inlets 7 and 8. A first gas inlet 7 provides the Ga melt 3 in the furnace 1 with a mixture of hydrogen gas (H2) and hydrochloric gas (HCl). HCl reacts with Ga and synthesizes gallium chloride (GaCI). GaCl molecules flow downward in gas phase toward the substrate 5 in the furnace 1. A second gas inlet 8 supplies a mixture of hydrogen gas (H2) and ammonia gas (NH3) to a middle space below the Ga boat 2 in the furnace 1. Reaction of gaseous GaCl with NH3 synthesizes gallium nitride (GaN) and deposits GaN molecules upon the substrate 5. An exhaustion gas is exhaled via a gas outlet 9 out of the furnace 1.
Another basic technology is the Epitaxial Lateral Overgrowth (ELO). Prior art {circle around (3)} and{circle around (4)} reported the ELO in detail. The ELO is described by referring to FIG. 2 to FIG. 4. In FIG. 2, the underlying blank signifies a (111) gallium arsenide single crystal substrate 10. A thin hatched mask 11 overlays the (111) GaAs monocrystalline substrate. The mask 11 should be made of a material which forbids GaN from piling upon. For example, the mask 11 is made of SiN (silicon nitride). Many small windows 12 are regularly distributed crosswise and lengthwise on the mask 11 in certain periods in accordance with a rule. A series of windows align with a period L in a GaAs [11xe2x88x922] direction. Another series of windows align with the same period by an off-set of L/2 in the same direction. Every three nearest neighbors form an equilateral triangle of a side of L. The distance between the neighboring parallel series is 3xc2xdL/2. The example of FIG. 2 has square windows. The shape of a window is arbitrary. The square windows can be replaced by round windows, striped windows or other polygon windows.
FIG. 3 shows a mask having many stripe windows arranged in a similar manner to the windows in FIG. 2. In FIG. 3, the underlaid blank means a (111) GaAs single crystal substrate wafer 10. The substrate wafer 10 is covered with the mask 11 having stripe-shaped (rectangular) windows 12.
A GaN film crystal is grown upon the masked GaAs wafer 10, for example, by the HVPE method. FIG. 4 shows a series of steps of piling the GaN layer upon the GaAs wafer. FIG. 4(1) is a section of the GaAs substrate wafer 10 covered with the mask 11 having the windows 12 before the growth. When the HVPE synthesizes GaN molecules, GaN grains grow only on the revealed portions of the GaAs substrate. FIG. 4(2) shows GaN cones 13 selectively formed upon the revealed GaAs parts. The mask has a function of excluding the piling of GaN. The mask 11 is free from GaN grains. The GaN cone 13 is a polygonal cone having {11xe2x88x9222} planes.
Thin vertical lines in the GaN cones 13 denote threading dislocations 14. The threading dislocations 14 extend in the growth direction. The defects are called xe2x80x9cthreading dislocationsxe2x80x9d 14 since the dislocations project upward by penetrating the successively growing layers. The underlying GaAs substrate crystal 10 determines crystallographical orientations of the GaN grains (cones) 13. FIG. 2 shows a GaAs [1xe2x88x9210] orientation and a GaAs [11xe2x88x922] orientation. GaN crystals grow along a c-axis in a [0001] orientation. In FIG. 2, a GaN [1xe2x88x92210] orientation coincides with the GaAs [1xe2x88x9210] orientation. A GaN [10xe2x88x9210] orientation coincides with the GaAs [11xe2x88x922] orientation.
When the height of the GaN cones attain to a critical level, the feet of the polygonal cones just fill the windows as shown in FIG. 4(2). Then, the GaN polygons extend in the horizontal directions over the mask 11. The GaN grains take a shape of a mesa, as shown in FIG. 4(3). Prevailing slanting planes on the mesas are {11xe2x88x9222} planes 16. The superficial planes 16 which are not parallel with the horizontal plane are called xe2x80x9cfacetsxe2x80x9d. The facets 16 appear on the mesas, since the GaN polygonal mesas grow in the horizontal directions from the slanting sides of the GaN cones of FIG. 4(2) on the mask 11. During the horizontal growth of the individual mesas, heights of the tops 15 of the individual mesas are a constant. There are gaps between the neighboring, independent GaN mesas. The GaN growth decreases the gaps between the separated GaN mesas. The threading dislocations 14 turn at 90 degrees and expand in the horizontal directions. The GaN mesas grow over the mask 11. Thus, the growing manner of FIG. 4(3) is called xe2x80x9cOvergrowthxe2x80x9d.
The prior art {circle around (1)} and {circle around (2)} reported a conspicuous decline of the density of the penetration dislocations in the extra parts over the mask 11. When a GaN crystal grows along the c-axis [0001], the threading dislocations extend also along the c-axis. When the c-axis growth has ended and the horizontal growth starts, the threading dislocations turn also in the horizontal directions. Thus, {circle around (1)} and {circle around (2)} asserted that the turn of the propagation directions reduces the effective density of the threading dislocations parallel with the c-axis [0001]. The reduction of the dislocations is an advantage of the ELO method.
Soon, the facets 16 of the neighboring mesas collide with each other at the middle lines between the adjacent windows. Further horizontal GaN growth raises the colliding levels of the adjoining mesas and reduces the gaps. Finally, all the gaps and all the {11xe2x88x9222} facets 16 disappear and all the neighboring mesas are unified into a common, flat GaN film crystal 18 as shown in FIG. 4(4). The horizontally extending dislocations collide together at middle planes 17 above the mask. The middle planes 17 store the ends of the threading dislocations. The planes are called xe2x80x9cplanar defect assembliesxe2x80x9d 17. Mirror plane growth is reduced on the C-plane (0001) by the two dimensional growth after disappearance of facets plane. Then, the GaN film 18 begins to grow uniformly upward. Thin threading dislocations start to extend upward again.
{circle around (1)} and {circle around (2)} reported that the planar defect assemblies 17 disappear when the film thickness attains to about 140 xcexcm. Since the planar defect assemblies 17 should be buried in the GaN film, the dislocations should be decreased afterward according to {circle around (1)} and {circle around (2)}.
FIG. 5 shows the same growth of the GaN film. FIG. 5(1) is the section of the GaAs substrate 10 covered with the mask 11 having the windows 12, which corresponds to FIG. 4(1). When the GaN epitaxial growth continues for a long time, the GaN crystal grows over the mask 11. Further the GaN crystal is grown upward to a tall GaN single crystal ingot 18 as shown in FIG. 5(2). The direction of the growth is a [0001] orientation (c-axis direction). The top of the GaN ingot is a (0001) plane which is called a xe2x80x9cC-planexe2x80x9d The top surface includes flat parts and rough parts. When a sufficiently thick GaN ingot 18 is grown, the GaN ingot is got off from the furnace 1. Then, the GaAs bottom substrate 10 and the mask 11 are eliminated. The GaAs can be removed by aqua regia. When the ingot has a thickness of one wafer, both surfaces or one surface are ground and polished. One C-plane GaN mirror wafer is obtained. When the ingot has a thickness for several times as thick as one wafer, the ingot are sliced into a plurality of GaN wafers 19 and the both surfaces or one surface of each wafer 19 are ground and polished. A plurality of GaN C-plane mirror wafers are obtained. The C-plane wafer is convenient, since the cleavage plane is vertical to the surfaces (C-planes) which facilitates to cut the wafer into a plenty of individual device chips and to form resonator mirrors in LDs.
There is an alternative to the method of FIG. 5 which makes GaN wafers directly from a GaAs substrate wafer.
{circle around (5)} Japanese Patent Application No. 10-102546 proposes another method which further grows a GaN single crystal ingot upon a seed GaN wafer 19 obtained by the steps of FIG. 5 by e.g., HVPE method, slices the ingot into a plurality of thin wafers and polishes the wafers. In this method, the seed wafer and the grown wafers have (0001) surfaces.
This new method enables us to produce GaN single crystal wafers on a commercial scale for the first time.
Some defects accompany the GaN wafers produced by the method of FIG. 5. The most serious problem is residuals of threading dislocations on the top surface. When the GaN crystal grows in a mode of maintaining a flat surface (C-plane surface), the threading dislocations accompany upward the growth without disappearing. Then, the top of the GaN wafer is always occupied by the residual threading dislocations.
As alleged by {circle around (1)} and {circle around (2)}, the ELO method succeeds in reducing the dislocations temporarily at an early stage of growth due to bending of the dislocations (FIG. 4(4)). Low dislocation density at the early step is an advantage of the ELO. But the effect is temporary. {circle around (1)} and {circle around (2)} were unaware of the recurrence of dislocations, because they stopped the ELO growth at the step of FIG. 4.(4).
When the GaN crystal is further grown up to a thickness more than several tens of micrometers, threading dislocations turn upward and extend in the c-axis direction, tracing the top surface. The planar defect assemblies 17 vanish at a height of about 140 xcexcm. The disappearance of the planar defect assemblies means to release the dislocations from the highly packed defect assemblies again. The dislocations turn to increase after the extinction of the planar defects. The surface of the GaN crystal is a flat smooth surface. But many dislocations are included in the mirror-like surface.
When the thickness of the GaN crystal reaches several centimeters, the top surface attains to a high density of dislocations of about 1xc3x97107 cmxe2x88x922. The dislocation density which has been once reduced by the first bending to the horizontal directions begins to increase by the second bending to the upward direction. The thick GaN ingot has high density dislocations on the top. GaN-LEDs would submit to the high dislocation density GaN wafers as a substrate.
If the GaN wafer were to used for making GaN laser diodes (LDs), the highly populating dislocations, the dislocations would lead the degradation of the GaN films. The rapid degeneration would raise the threshold current and would curtail the lifetime. The ELO-made GaN wafers are not suitable for LDs yet.
The inventors of the present invention have scrutinized the growth modes. In the following description, inclining superficial parts except the (0001) C-plane on the top are called xe2x80x9cfacet-planexe2x80x9d. Thus, the top surface of a growing crystal has C-plane parts and facet-plane parts. In FIG. 4(2) and (3), the slanting side surfaces are all facet-planes 16. As shown in FIG. 4(4), the facet-planes {11xe2x88x9222} of isolated mesas meet with each other and are unified on the mask at a height of about 6 xcexcm. The aggregation decreases the dislocations. Then, the unified flat GaN crystal is further grown in the HVPE apparatus which is controlled to maintain the C-planar mirror top surface. In the meantime the dislocations increase again. GaN film samples of a thickness from 0.2 mm to 0.6 mm are produced by the above-mentioned method (HVPE and ELO). The dislocation density of each sample is measured.
Although the ELO decreases the dislocations, the measured dislocations are higher than 1xc3x97107 cmxe2x88x922 at the top surface for the samples. The reason of the recurrence of dislocations is the release of the dislocations once trapped in the planar defect assemblies by an increment of the thickness.
As long as the two dimensional growth which maintains a flat, smooth mirror surface (C-plane) continues, the dislocations extend upward without disappearing, accompanying the vertical growth. The two dimensional growth with the mirror surface contains no mechanism of extinguishing dislocations. Dislocations always climb to catch up to the top surface. If there is no mechanism of killing dislocations, low dislocation density crystal cannot be obtained. The inventors of the present invention thought of a new crystal growth method containing a dislocation annihilation mechanism. If the mechanism of decreasing defects is included in a new growth technique, the technique will enable us to make a low dislocation density GaN single crystal. From the standpoint, the inventors contrived,
{circle around (6)} Japanese Patent Application No.11-273882.
This prior invention of the present inventors tried to make a low dislocation density GaN single crystal by maintaining a rough top surface containing facets without burying facets and forming pits containing facets on the top. The facets sweep the dislocations into the pits having facet walls. The pits absorb the dislocations. The dislocations are gathered in the pits. Since the total sum of dislocations is kept constant, the distribution of the dislocations in other portions except the facet pits is reduced.
The invention has an excellent effect of reducing substantially dislocations in a GaN crystal by producing facet structure (roughed surface, facet pits) on the top, guiding dislocations toward the facet pits by the ELO growth and accumulating the dislocations in the pits. The contrivance succeeded in obtaining a low-dislocation density GaN crystal by gathering dislocations into bundles.
Hitherto prior art has been described. General concepts regarding crystallography are described for clarifying the idea of the present invention.
[Identification of Crystallographic Orientations]
Gallium nitride (GaN) belongs to a hexagonal symmetry group. It is rather difficult to identify the crystal orientations. The description of the present invention requires expressions of orientations (directions) and planes of a hexagonal crystal. To avoid confusion for understating of the new idea, the identification of orientations and planes is confirmed. The hexagonal symmetry has three equivalent horizontal axes inclining at 120 degrees to each other and a vertical axis perpendicular to the three. Two axes among the three horizontal axes are called an xe2x80x9ca-axisxe2x80x9d and a xe2x80x9cb-axisxe2x80x9d. The third axis has no definite name, which is inconvenient. Here, the third horizontal axis is called a xe2x80x9cd-axisxe2x80x9d. The unique vertical axis is called a xe2x80x9cc-axisxe2x80x9d. There are a three index expression and a four index expression. This description employs the four index expression making use of four redundant indices for a-axis, b-axis, d-axis and c-axis. The lengths of the unit a-axis, b-axis and d-axis are equal. The length is denoted by xe2x80x9caxe2x80x9d. The length of the c-axis is denoted by xe2x80x9ccxe2x80x9d. The ratio a/c depends upon the matters forming hexagonal crystals.
The mirror indices define planes and orientations in an individual manner and a collective manner. In a periodic crystal, a crystallographical plane means a set of an indefinite large number of identical parallel planes. When the plane nearest to the origin cuts the a-, b-, d-, and c-axes at a/h, b/k, d/m and c/n, the plane is expressed by an expression (hkmn), where h, k, m and n are integers (plus, minus or 0) which are called mirror indices. The mirror index is a denominator of the segment. The bracket contains no comma. FIG. 6 shows definitions of h, k and m in the horizontal abd-plane. The a-axis, b-axis and d-axis are half straight lines starting from the origin O. The inclination angles of the axes are 120 degrees. The plane slashes the a-axis (or the negative extension) at a/h, the b-axis (or the negative extension) at b/k and the d-axis (or the negative extension) at d/m. In the example, h and k are positive but m is negative. All three negative indices and all three positive indices are denied.
Different brackets signify different modes of orientations or planes. A round bracket (hkmn) means an individual plane which cuts the a-, b-, d-, and c-axes at a/h, b/k, d/m and c/n. A wavy bracket {hkmn} means a set of collective planes which can be attained by all the allowable crystal hexagonal symmetry operations from the individual (hkmn) plane. A square bracket [hkmn] is an expression of an individual orientation (direction). The [hkmn] orientation (direction) is vertical to the (hkmn) plane. Namely, a plane is always orthogonal to the corresponding orientation having the same mirror indices also in the hexagonal symmetry like other symmetry groups. A key bracket  less than hkmn greater than  is a collective expression of the orientations which can be attained by all the allowable crystal hexagonal symmetry operations from the individual orientation [hkmn]. Thus, the concrete members contained in the collective expressions {hkmn} and  less than hkmn greater than  depend upon the object crystal. The hexagonal symmetry itself does not determine the members of the collective expressions.
[hkmn]=individual orientation.  less than hkmn greater than =collective orientation.
(hkmn)=individual plane. {hkmn}=collective plane.
If the object crystal has three-fold (rotation) symmetry, the collective expression {hkmn} is the same as {kmhn} and {mhkn} which are obtained by changing the three indices cyclically. If the object crystal has inversion symmetry, the {hkmn} plane is identical to {xe2x88x92hxe2x88x92kxe2x88x92mxe2x88x92n}. Crystallography attaches an upperline to a numeral for signifying a negative number. But since the upperline is forbidden, a front minus sign is used instead of the upperline, for example, xe2x88x92h, xe2x88x92k, xe2x88x92m or xe2x88x92n. The c-axis index xe2x80x9cnxe2x80x9d should be discriminated from the symmetric h, k and m.
Three mirror indices h, k and m on the horizontal plane are not independent. The freedom is not three but two. The mirror indices h, k and m have a zero-sum rule,
h+k+m=0.xe2x80x83xe2x80x83(1) 
FIG. 7 gives a brief proof of the zero-sum rule. The origin is denoted by xe2x80x9cOxe2x80x9d. Points B and D are allotted onto the b-axis and the d-axis for satisfying OB=OD. Line OH is a negative extension of the a-axis. Point H is the cross point of Line BD with Line OH (xe2x88x92a-axis).  less than OBH= less than ODH=30xc2x0. An arbitrary line passing through point H crosses at F and E with OD and OB respectively. Line EHF denotes a crosses segment of an object crystallographical plane with the abd-plane. Lengths are denoted by OE=Y, OF=Z, OH=xe2x88x92X(xe2x88x92X greater than 0). An inclining angle is designated by  less than DHF=0. Thus,  less than OFH=30xc2x0xe2x88x92xcex8,  less than OEH=30xc2x0+xcex8,  less than OHF=90xc2x0+xcex8, and  less than OHE=90xc2x0xe2x88x92xcex8. The sine theorem gives the following relations,
xe2x88x92X=Y sin less than OEH/sin less than OHE=Y sin(30xc2x0+xcex8)/sin(90xc2x0xe2x88x92xcex8) 
xe2x80x83and
xe2x88x92X=Z sin less than OFH/sin less than OHF=Z sin(30xc2x0xe2x88x92xcex8)/sin(90xc2x0+xcex8).                                                         -              X                        /            Y                    -                      X            /            Z                          =                                            sin              ⁡                              (                                                      30                    ⁢                    xc2x0                                    +                  θ                                )                                      /                          sin              ⁡                              (                                                      90                    ⁢                    xc2x0                                    -                  θ                                )                                              +                                    sin              ⁡                              (                                                      30                    ⁢                    xc2x0                                    -                  θ                                )                                      /                          sin              ⁡                              (                                                      90                    ⁢                    xc2x0                                    +                  θ                                )                                                                            =                                            {                                                sin                  ⁡                                      (                                                                  30                        ⁢                        xc2x0                                            +                      θ                                        )                                                  +                                  sin                  ⁡                                      (                                                                  30                        ⁢                        xc2x0                                            -                      θ                                        )                                                              }                        /            cos                    ⁢                      xe2x80x83                    ⁢          θ                                        =                              2            ⁢                          xe2x80x83                        ⁢            sin            ⁢                          xe2x80x83                        ⁢            30            ⁢            xc2x0                    =          1.                    
Then,
1/X+1/Y+1/Z=0. 
The definition of the mirror indices substitute X, Y and Z by X=a/h, Y=b/k and Z=d/m. Three a-, b- and d-axes have the same length (a=b=d). Thus,
h+k+m=0. 
The zero-sum rule in the four index expression in the hexagonal crystals is proved.
A plane distance is a distance between the nearest two planes belonging to the same plane group. How is the plane distance denoted in the hexagonal symmetry? For simplicity, the planes (n=0) parallel with the c-axis are first considered. The plane distance of the plane {hkm0} is given by,                     d        =                                                                              3                  2                                            ⁢              a                                                                        h                  2                                +                                  k                  2                                +                                  m                  2                                                              .                                    (        2        )            
Although h, k and m are essentially two dimensional parameters, the expression resembles the three dimensional case. Modification is contained in the coefficient (3/2)xc2xd.
Two planes which are parallel to the c-axis cross on lines parallel to the c-axis. The crossing angle "THgr" of two planes (hkm0) and (stu0) is given by                               cos          ⁢                      xe2x80x83                    ⁢          Θ                =                                            hs              +              kt              +              mu                                                                                            h                    2                                    +                                      k                    2                                    +                                      m                    2                                                              ⁢                                                                    s                    2                                    +                                      t                    2                                    +                                      u                    2                                                                                .                                    (        3        )            
This formula which holds only on a two dimensional c-plane is superficially similar to the three dimensional crossing angle formula in the cubic symmetry. When two planes parallel with the c-axis are orthogonal to each other, the sum of the products of the indices is zero.
hs+kt+mu=0.xe2x80x83xe2x80x83(4) 
This is a perpendicular condition.
The planes (000n) having a normal parallel to the c-axis are called xe2x80x9cC-planexe2x80x9d. xe2x80x9cnxe2x80x9d means the division number of a unit c-axis. A unit c-axis contains n sheets of the (000n) plane. All planes {hkm0} are perpendicular to the c-planes (000n).
FIG. 8 shows a (1xe2x88x92100) plane and a (11xe2x88x9220) plane. The planes are parallel to the c-axis. The (1xe2x88x92100) plane passes a positive 1 on the a-axis, a negative 1 on the b-axis but would meet with the d-axis at an infinitive distance. Thus, the plane can be denoted by (1xe2x88x92100). The (11xe2x88x9220) plane passes a positive 1 on the a-axis, a positive 1 on the b-axis and a negative half on the d-axis. Therefore, the plane can be denoted by (11xe2x88x9220). The planes satisfy Eq.(4). The (11xe2x88x9220) plane is perpendicular to the (1xe2x88x92100) plane. These two planes have important roles. The {1xe2x88x92100} planes are collectively called xe2x80x9cM-planesxe2x80x9d. The {11xe2x88x9220} planes are collectively called xe2x80x9cA-planesxe2x80x9d. M-plane includes six different planes (1xe2x88x92100), (10xe2x88x9210), (01xe2x88x9210), (xe2x88x921100), (xe2x88x921010) and (0xe2x88x92110). These planes can form the sides of a regular hexagon. The neighboring two planes meet with each other at 120 degrees. The individual M-planes incline to each other at 60 degrees, 120 degrees or 180 degrees.
A set of only M-planes can structure a regular hexagon.
Similarly A-planes {11xe2x88x9220} include six different individual planes which can form the sides of a regular hexagon. The individual A-planes incline to each other at 60 degrees, 120 degrees or 180 degrees like M-planes. A set of only A-plane can structure a regular hexagon.
Although it is said that the M-plane is at a right angle to the A-plane, all the M-planes do not incline at 90 degrees to all the A-planes. A selected set of, for example, a (1xe2x88x92100) plane and a (11xe2x88x9220) plane satisfies the orthogonality condition. In general, the angles between the M-planes and the A-planes are 30 degrees, 90 degrees, 150 degrees, 210 degrees, 270 degrees or 330 degrees. The basic difference between the A-planes and the M-planes is not 90 degrees but 30 degrees.
Six A-planes and six M-planes can form the sides of a regular dodecagon. The {11xe2x88x922n} planes are obtained by inclining the A-planes to the c-axis. An assembly of the A-deriving {11xe2x88x922n} planes can form a regular hexagonal cone. The {1xe2x88x9210} planes are obtained by inclining the M-planes to the c-axis. An assembly of the M-deriving {1xe2x88x9210n} planes can form another regular hexagonal cone. A set of six A-deriving {11xe2x88x922n} and six M-deriving {1xe2x88x9210n} planes can form a regular dodecagonal cone.
The inventors have succeeded in growing a low-dislocation density GaN single crystal by maintaining rough facet-planes upon the growing surface in accordance with the teaching of {circle around (6)} Japanese Patent Application No.11-273882. This method, however, is subject to accumulation of dislocations at the bottoms of the facet-pits. High dislocation density bundles follow down the facet-pits. Except the bottoms of the facet-pits, the GaN enjoys low-dislocation density.
The GaN of {circle around (6)} has the advantage of having wide regions of low dislocation density except the localized facet-pits with concentrated dislocations. The localized accumulation of dislocations decreases the device properties and the yield. If a GaN crystal is grown under the condition of keeping facets on the top surface along the teaching of {circle around (6)}, bundles of dislocations accompany the bottoms of the facet-pits. The regions are degraded by the concentrated dislocations. The LDs fabricated upon the dislocation accumulated regions would be rejected at the inspection, which would decrease the yield. If the LDs are not rejected, the LD""s lifetime is shortened. The accumulated dislocations impede the GaN from cleaving by disturbing the regularity of lattices. {circle around (6)} cannot give a final solution because the sum of dislocations is not reduced.
A true solution of the problems should be realized by decreasing penetration dislocations substantially and by removing bundles of dislocations from the surface of the GaN crystal.
Another problem of the GaN crystal having highly accumulated dislocations is disorder of cleavage. Bundles of penetration dislocations locally induce strong stress concentration. When LD devices have been fabricated on a GaN wafer, the wafer will be scribed and cleaved into individual LD chips. Since the GaN is a single crystal, the cleaved plane should be mirror flat. Strong stress concentration, however, prohibits cleaved edges from being flat planes. The cleaved edges of {circle around (6)} show shell-like wavy texture instead of mirror flatness. The wavy texture originates from the ununiformely populating dislocations realized by the facet-maintaining growth. The concentration of dislocations perturbs natural cleavage.
The disorder of cleavage should result from random distribution of inner stress caused by the concentration of dislocations. If the LDs made on a GaN wafer have rough sides caused by the perturbed cleavage, the sides should be polished further for obtaining mirror sides of a resonator. The extra step of polishing would raise the manufacturing cost. High rigidity would require a long time for polishing. If so, the GaN substrate would not be superior to the sapphire substrate at all. Highly expensive GaN would be overwhelmed by inexpensive, accustomed sapphire.
The solution of the problems requires both the reduction of threading dislocations and the extinction of bundles of dislocations on the surface. Disappearance of the dislocation bundles should expel the disorder of cleavage planes. One purpose of the present invention is to provide a gallium nitride wafer free from localized bundles of dislocations. Another purpose of the present invention is to provide a gallium nitride wafer having clear cleavage. A further purpose of the present invention is to provide a method of making a gallium nitride wafer without bundles of dislocations on the surface. Another purpose of the present invention is to provide a method of making a gallium nitride wafer immune from the disorder of cleavage.
Here, the direction of the crystal growth is denoted by xe2x80x9cgxe2x80x9d. The direction of the extending dislocations is denoted by xe2x80x9cqxe2x80x9d. A first invention is to make a GaN substrate by slicing in a plane S which is parallel to the crystal growing direction g or dislocation extending direction q. Since the slicing plane S is parallel to the dislocation extension direction q, the dislocations run horizontally on the surface of the GaN substrate. Most of the dislocations do not appear on the surface but run in the inner space of the crystal. Then, the dislocation density is reduced on the surface.
The gist of the present invention is to reduce dislocations appearing on the surface by coinciding the dislocations extending directions to the surface. Although the GaN substrate includes a great many dislocations in the depth, a small portion of the dislocations appears on the surface due to the parallelism of the dislocations and the surface. Inner dislocations have no influence upon manufacturing devices (LDs and LEDs). What is important is the dislocations appearing on the surface. The GaN substrate of the present invention which has a small number of dislocations on the surface can be a suitable substrate for producing devices.
The purpose is the reduction of superficial dislocations. The solution is to slice a GaN crystal in a cut plane parallel with the dislocation extension q or growing direction g into a substrate. xe2x80x9cg parallel to Sxe2x80x9d or xe2x80x9cq parallel to Sxe2x80x9d can shortly express the idea of the present invention. A symbol xe2x80x9c∥xe2x80x9d denotes parallelism. By the symbol, the present invention is represented by,
q∥S,xe2x80x83xe2x80x83(5) 
or 
g∥S.xe2x80x83xe2x80x83(6) 
xe2x80x9cqxe2x80x9d and xe2x80x9cgxe2x80x9d are one dimensional lines. xe2x80x9cSxe2x80x9d means a two dimensional plane. The surface S is not determined by the restriction of being parallel with q. S still has an extra freedom of rotation by 180 degrees around q. Fortunately, the freedom widens the range of choice of the cutting plane.
The dislocation extension directions sometimes disperse isotropically. The dislocation extending directions are nearly parallel at other times. When the dislocations disperse isotropically, the present invention cannot be applied. Although the dislocation extension directions q are not determined uniquely, the dislocations dispersion has an average direction on the plane. When the dislocation directions diverge but an average direction of the dislocations is defined, the present invention is available.
When the extensions of dislocations can be uniquely defined, Eq.(5) determines the direction of the slicing plane. Thus, irrespective of the growth direction g, a cutting surface S satisfying q∥S does exist. The growing direction g determines whether the dislocations disperse or converge. The restriction q∥S determines the cutting plane S for the growing direction g having the converging dislocations.
FIG. 9(1) to FIG. 9(4) describe steps of a prior cutting way of a GaN crystal. A GaN crystal ingot is grown (g∥c) in the c-axis direction on a sapphire or a GaAs substrate. Dislocations extend also in the c-axis direction. Then the prior ingot is sliced in the horizontal plane which is parallel to the growing surface (C-plane). The slicer cuts many dislocations vertically. A Great many dislocations appear on the cut surface, as shown in FIG. 9(3). FIG. 9(4) is a plan view of the prior art substrate having plenty of dotted dislocations. Since the substrate is cut in plane vertical to the dislocations, all the dislocations appear on the surface of the substrate. The prior substrate is suffering from plenty of dislocations. The prior one of FIG. 9(4) is improper to the substrate for making devices.
FIG. 10 shows the slicing of the present invention. An upward arrow designates the growth direction. Thin lines denote dislocations in parallel to the growth direction (g). This invention slices the GaN ingot in a plane parallel to the dislocations (q∥S). The cutting planes of FIG. 10(1) are vertical to the prior cutting planes of FIG. 9(2). The top surface is the growing plane which is orthogonal to the growing direction. FIG. 10(2) and FIG. 10 (3) show the threading dislocations running in parallel with the surface of the substrate. The density of the dislocations appearing on the surface is greatly reduced by the mode of slicing. Although the total dislocations do not decrease, the superficial dislocations staying on the surface are reduced. The dislocations which have an influence upon producing devices are not the total of the dislocations but the superficial dislocations lying on the surface. Instead of concentrating dislocations into tiny bundles, this invention succeeds in substantially reducing dislocations by laying down dislacations in the horizontal directions. Since the crystal contains no localized bundle of dislocations, the problem of the rugged cleaved planes is also solved by the present invention. FIG. 9(4) and FIG. 10(3) clarify the difference between prior art {circle around (6)} and the present invention.
If the growing direction coincides with the dislocation extension (g=q), the present invention obtains another expression that the slicing plane S should be parallel to the growth direction (g∥S). Eq.(6) denotes the same condition.
In such a case (g=q), FIG. 10(1) exhibits the cutting plane S being parallel to the growth direction g. The present invention includes the case of S∥g. If g=q, q∥S is equivalent to g∥S.
Someone may think that if q∥S is equivalent to g∥S, one should be omitted in the expression for avoiding redundancy. But if two conditions are equivalent, elimination of one is undesirable. When a single crystal is grown by some method, the growing direction g is obvious. The direction g is perpendicular to the substrate. On the contrary, the extensions of threading dislocations are not easily confirmed. The dislocations are detected by slicing the ingot into sheet crystals, etching the sheet crystals by a special etchant revealing dislocations and observing the appearing dislocations. The definition through the dislocation extensions incurs a difficulty of determining dislocation extensions. It is more convenient to define the present invention by the growing direction xe2x80x9cgxe2x80x9d.
This invention can be applied even when the growing direction deviates from the dislocation extensions (gxe2x89xa0q). In case of gxe2x89xa0q, q∥S has priority over g∥S.
The concept xe2x80x9creductionxe2x80x9d of dislocations is now clarified, since the purpose of the present invention is to make low-dislocation density GaN substrates. The change of cutting planes from the conventional orthogonal planes to parallel planes to the growing direction does not decrease the inherently-lying dislocations. The intrinsic dislocations survive in the crystal despite the cutting planes. The sum of dislocations is intact after the cutting. What makes an influence upon the device performance is not the deep (intrinsic) dislocations hidden in the bulk but the superficial dislocations appearing on the surface. The present invention aims not at reducing all the dislocations in the bulk but at reducing only the dislocations appearing on the surface. The word xe2x80x9creductionxe2x80x9d signifies the reduction of the superficial dislocations in the present invention. xe2x80x9cLow-dislocation densityxe2x80x9d means that the dislocations appearing on the surface is of low density.
Fortunately, the horizontally running dislocations do not perturb the cleavage property, since the dislocation extensions are parallel to the surface of the substrate.
The problem of the density of threading dislocations is simple. The dislocation density on a surface orthogonal to the dislocation extension is denoted by xe2x80x9cExe2x80x9d. E is the number of dislocations included in a unit area which is perpendicular to the dislocations. The number of dislocations which pass a unit area which slants at an inclination angle xcfx86 to the dislocations is in proportion to cos xcfx86. E cos xcfx86 is the dislocation density on the slanting plane inclining at xcfx86 to the dislocation direction. The gist of the present invention is to slice the GaN ingot in planes which are parallel to the extension of the threading dislocations. Namely, the invention realizes xcfx86=90 degrees which gives cos xcfx86=0. cos xcfx86=0 means the reduction of dislocations on the surface of the substrate in the present invention. Geometric consideration clarifies the low density of dislocations on the surface of the substrate which is obtained by slicing in the cutting plane which is parallel to the dislocation extension.
Deliberate experiments enabled the inventors to discover a fortunate property that favorable p-q equivalence (q=g) holds on three special growing orientations. The growing direction xe2x80x9cgxe2x80x9d is equal to the dislocation extension xe2x80x9cqxe2x80x9d in the three growing orientations. The discovered special growing orientations are  less than 1xe2x88x92100 greater than ,  less than 11xe2x88x9220 greater than  and  less than 0001 greater than . For convenience, symbols m, a and c are allotted to the selected growing directions, i.e., m= less than 1xe2x88x92100 greater than , a= less than 11xe2x88x9220 greater than  and c= less than 0001 greater than . The p-q equivalence (q=g) is a very useful property. Other growing directions are not favored with the p-q equivalence. When a GaN crystal is grown in the other directions, dislocations extensions deviate from the growing directions. The planes orthogonal to the selected growing directions m, a and c are designated by
M={1xe2x88x92100}, A={11xe2x88x9220} and C={0001}.xe2x80x83xe2x80x83(7) 
The growing directions m, a and c are orthogonal to the planes M, A and C respectively. When a GaN crystal is grown in m-, a- or c-directions, the p-q equivalence (q=g) allows the present invention to determine suitable slicing planes S which are parallel to the growing direction g.
Fortunately, the special planes can be orthogonal to each other by selecting proper sets of M, A and C-planes. The orthogonality among three special planes is another favorable property which provides this invention with practical utility. Since GaN is hexagonal on the normal condition, there are six equivalent planes which can be transformed by the allowed symmetry operations. The M-plane includes six equivalent planes and A-plane also contains six equivalent planes. The C-plane includes two planes. All C-planes are orthogonal to all A-planes. All C-planes are orthogonal to all M-planes. An arbitrary member of the A-planes is orthogonal to two of the M-planes. An arbitrary member of the M-planes is orthogonal to two of the A-planes. FIG. 11 shows a cubic consisting of an A-plane (11xe2x88x9220), an M-plane (1xe2x88x92100) and a C-plane (0001) which are orthogonal to each other. Hexagonal symmetry has a surprising property of the orthogonality of three low mirror index planes. The present invention makes the best use of the orthogonal property.
There may be another growing direction ensuring the p-q equivalence than the m, a and c-directions. If so, the present invention can be applied to the direction.
All the probable directions do not have equal tendency of making a single crystal. Some directions are more suitable but other directions are less suitable for growing single crystals in their directions. Favorably, the three low index orientations are all easy growth directions. At present, neither A-plane GaN crystal nor M-plane GaN crystal is available yet. Few C-plane GaN single crystals have been made due to immature technology. However, the inventors have confirmed the easy growth of the three orientations. Namely, m, a and c can be chosen as a growing direction g.
g=m, a, cxe2x80x83xe2x80x83(8) 
On the contrary, the surfaces of the GaN crystals are determined by the requests of device makers. Since the GaN crystal is the substrate wafer for producing devices, low index substrates of M-substrates, A-substrates and C-substrates will be required in the main.
Cleavage planes of GaN are a C-plane (0001) and an M-plane {1xe2x88x92100}. The existence of cleavage is one of the strong point of GaN. If GaN LDs are fabricated upon an A-plane substrate (A-substrate in short), natural cleavage can form parallel mirrors of two sides (M-planes or C-planes) of an LD chip as a resonator. If GaN LDs are fabricated upon an M-plane substrate (M-substrate in short), natural cleavage can form parallel mirrors of two sides (C-planes) of an LD chip as a resonator. However, there is neither A-substrate nor M-substrate of a practical size. If GaN LDs are fabricated upon a C-plane substrate (C-substrate in short), natural cleavage can form parallel mirrors of two sides (M-planes) of an LD chip as a resonator. Preferable slicing planes S are,
S=M, A, C.xe2x80x83xe2x80x83(9) 
FIG. 12 demonstrates the concept of the present invention that low-dislocation GaN substrates are obtained by slicing a GaN crystal ingot in planes xe2x80x9cSxe2x80x9d parallel to the growing direction xe2x80x9cgxe2x80x9d. xe2x80x9cSxe2x80x9d denotes a cutting plane, xe2x80x9cgxe2x80x9d is a growing direction. Growth surface on the front is orthogonal to the growing direction g. The cutting planes S are orthogonal to the growth surface. The orthogonality of the growing surface to the slicing planes is equivalent to the parallelism of the growing direction g to the cutting surface S(g∥S). Both are directed to the same idea of the present invention. The m-growing direction requires C-cutting planes or A-cutting planes. The a-growing direction requires M-cutting planes or C-cutting planes. The basic condition g∥S can alternatively be expressed by a rule that a GaN ingot should be cut along the growing direction g.
The above described single step compensation of the growth and slice is a basic concept of the present invention. A heavier significance lies on reduction of dislocations based upon multiple growths. The multiple growths mean repetitions of slicing a GaN ingot along dislocations into seeds and growing a GaN ingot on the GaN seed. A single cycle of growth and slice produces a low-dislocation seed having few dislocations on the surface as shown in FIG. 10(2). If another GaN ingot is grown on the low-dislocations density seed of FIG. 10 (2), the GaN ingot would enjoy low-dislocation density, since dislocations in the growing crystal succeed the intrinsic dislocations on the surface of the seed.
A low dislocation density seed allows this invention to produce a GaN crystal of a dislocation density as low as the seed. The parallel slicing denoted by q=S or g=S decreases the dislocation density further. Namely, a change of the growth directions at 90 degrees in double growths enables the present invention to reduce dislocations. The reduction of dislocations is not superficial but substantial. True reduction of dislocations is accomplished by multiple growths which vary the growing directions g. The reduction of dislocations by the zigzag repetitions of growth and slice is another strong point of the present invention. As shown in FIG. 12, a second growth in the w-direction brings about a true decline of dislocations.
In addition to double growth, this invention is realized by higher times of zigzag growths, for example, zigzag triplet growths, zigzag quadruple growths or so. Three different growing directions m, a and c enable multiple growths to accomplish a variety of sets of planes and orientations.
Motives for which the inventors hit this invention are described. The inventors were aware that the dislocations have a tendency of extending in the same direction as the growth in a GaN growth, for example, in GaN film growth on sapphire substrates which are still prevalent to make blue-light GaN/sapphire LEDs. Enormous dislocations extending in a c-direction are observed in the GaN film growing in the c-direction on the sapphire.
From the observation, the inventors hit an idea for the reduction of dislocations by coinciding a surface with dislocations through slicing a GaN crystal in the planes which are parallel to the growing direction. The fundamental idea of the invention is to reduce dislocations by making a GaN crystal having dislocations aligning in a direction, slicing the GaN crystal in the dislocation-aligning plane and obtaining low-density dislocation GaN. This is entirely a novel idea. Who has noticed the way of slicing a crystal in the direction parallel to the growth? Nobody was aware of the growth-parallel-slicing of a crystal.